Strategic Communication Between Prospect Theoretic Agents over a Gaussian Test Channel

Abstract: In this paper, we model a Stackelberg game in a simple Gaussian test channel where a human transmitter (leader) communicates a source message to a human receiver (follower). We model human decision making using prospect theory models proposed for continuous decision spaces. Assuming that the value function is the squared distortion at both the transmitter and the receiver, we analyze the effects of the weight functions at both the transmitter and the receiver on optimal communication strategies, namely encoding at the transmitter and decoding at the receiver, in the Stackelberg sense. We show that the optimal strategies for the behavioral agents in the Stackelberg sense are identical to those designed for unbiased agents. At the same time, we also show that the prospect-theoretic distortions at both the transmitter and the receiver are both larger than the expected distortion, thus making behavioral agents less contended than unbiased agents. Consequently, the presence of cognitive biases increases the need for transmission power in order to achieve a given distortion at both transmitter and receiver.